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A326029
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Number of strict integer partitions of n whose mean and geometric mean are both integers.
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8
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0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 3, 1, 3, 1, 1, 3, 6, 1, 3, 1, 2, 1, 1, 1, 3, 1, 6, 1, 5, 1, 2, 2, 2, 4, 3, 1, 9, 1, 1, 3, 1, 1, 4, 1, 4, 2, 6, 1, 6, 1, 3, 7, 4, 2, 5, 1, 10, 1, 3, 1, 9, 3
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OFFSET
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0,11
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LINKS
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EXAMPLE
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The a(55) = 2 through a(60) = 9 partitions:
(55) (56) (57) (58) (59) (60)
(27,16,9,2,1) (24,18,8,6) (49,7,1) (49,9) (54,6)
(27,25,5) (50,8) (48,12)
(27,18,12) (27,24,9)
(27,24,6,2,1)
(36,12,9,2,1)
(36,9,6,4,3,2)
(24,18,9,6,2,1)
(27,16,9,4,3,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}]
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CROSSREFS
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Partitions with integer mean and geometric mean are A326641.
Strict partitions with integer mean are A102627.
Strict partitions with integer geometric mean are A326625.
Non-constant partitions with integer mean and geometric mean are A326641.
Subsets with integer mean and geometric mean are A326643.
Heinz numbers of partitions with integer mean and geometric mean are A326645.
Cf. A051293, A067538, A067539, A078175, A082553, A316413, A326027, A326623, A326644, A326646, A326647.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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